A broad class of engineering problems including penetration, impact and large rotations of solid bodies causes severe numerical problems. For these problems, the constitutive equations are history dependent so material points must be followed; this is difficult to implement in an Eulerian scheme. On the other hand, purely Lagrangian methods typically result in severe mesh distortion and the consequence is ill conditioning of the element stiffness matrix leading to mesh lockup or entanglement. Remeshing prevents the lockup and tangling but then interpolation must be performed for hmtory dependent variables, a process which can introduce errors. Proposed here is an extension of the particle-in-cell method in which particles are interpreted to be material points that are followed through the complete loading process. A fixed Eulerian grid provides the means for determining a spatial gradient. Because the grid can also be interpreted as an updated Lagrangian frame, the usual convection term in the acceleration associated with Eulerian formulations does not appear. With the use of maps between material points and the grid, the advantages of both Eulerian and Lagrangian schemes are utilized so that mesh tangling is avoided while material variables are tracked through the complete deformation history. Example solutions in two dimensions are given to illustrate the robustness of the proposed convection algorithm and to show that typical elastic behavior can be reproduced. Also, it is shown that impact with no slip is handled without any special algorithm°f or bodies governed by elasticity and strain hardening plasticity. *The work described in this report was performed for Sandia National Laboratories under Contract No. AC-1801 M ,S]ER i DISTRtP.__,UTION OF THIS DOCUMENT 18 UNLIMITED This page left blank. TABLE OF CONTENTS°S UMMARY vii 1.0 INTRODUCTION 1 2.0 GOVERNING EQUATIONS 3 3.0 MIXED WEAK FORM OF GOVERNING EQUATIONS 5 4.0 THE CONVECTIVE PHASE 9 5.0 GENERATION OF MATERIAL POINTS 1| 6.0 NUMERICAL ALGORITHM 13 7.0 NUMERICAL EXAMPLES 15 7.1 Rotation Test 7.2 Vibrating solid elastic cylinder 7.3 Impact of two elastic bodies 7.4 Bouncing Bar 7.5 Impact of two inelastic bodies 24 7.6 Impact of an elastic disk with a strain-hardening disk 24 8.0 CONCLUSION 9.0 REFERENCES

Multi-Agent Path Finding (MAPF) is the challenging problem of computing collision-free paths for multiple agents. Algorithms for solving MAPF can be categorized on a spectrum. At one end are (bounded-sub)optimal algorithms that can find high-quality solutions for small problems. At the other end are unbounded-suboptimal algorithms that can solve large problems but usually find low-quality solutions. In this paper, we consider a third approach that combines the best of both worlds: anytime algorithms that quickly find an initial solution using efficient MAPF algorithms from the literature, even for large problems, and that subsequently improve the solution quality to near-optimal as time progresses by replanning subgroups of agents using Large Neighborhood Search. We compare our algorithm MAPF-LNS against a range of existing work and report significant gains in scalability, runtime to the initial solution, and speed of improving the solution.

As recently studied, field-programmable gate arrays (FPGAs) suffer from growing Hardware Trojan (HT) attacks, and many techniques, e.g., register-transfer level (RTL) code-based analyzing, have been presented to detect HTs on FPGAs. However, for most of the FPGA end users, they can only obtain bitstream, rather than the RTL code. Therefore, we present a new FPGA reverse engineering tool-chain. It can precisely transform the FPGA bitstream to an RTL code and therefore assists in HT detection. In detail, we first construct an integrated database involving the FPGA architecture information and the bitstream mapping information. Then, we build two tools, namely, bitstream reversal tool (BRT) and netlist reversal tool (NRT). They can be combined together to retrieve the RTL code from the FPGA bitstream in moderate time. To demonstrate the effectiveness of our tool-chain, we evaluate it qualitatively and quantitatively by using two benchmarks (ISCAS'85 and ISCAS'89) and three real applications (8051 core, 68HC08, and AES). Our tool-chain is comprehensive since it covers all the reverse engineering stages, from bitstream to netlist and from netlist to code, without any support from other tools. Moreover, it rebuilds the netlist with a 100% correct rate and retrieves RTL code, which is exactly, functionally equivalent to the original one for all our benchmarks. To the best of our knowledge, it is the first tool that can perform integrated, precise reverse engineering for FPGAs, paving the way for the netlist-/code-based HT detection. INDEX TERMS FPGA, reverse engineering, bitstream, hardware trojan.

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